Chapter 26 - Potential and Field - Exercises and Problems - Page 738: 15

(a) $E_x = 27~V/m$ (b) $E_x = 3.7~V/m$

(a) $V = 100~e^{-2x}~V$ $\frac{dV}{dx} = -200~e^{-2x}~V/m$ We can find $E_x$: $E_x = -\frac{dV}{dx}$ $E_x = -(-200~e^{-2x})~V/m$ $E_x = 200~e^{(-2)(1.0)}~V/m$ $E_x = 27~V/m$ (b) We can find $E_x$: $E_x = -\frac{dV}{dx}$ $E_x = -(-200~e^{-2x})~V/m$ $E_x = 200~e^{(-2)(2.0)}~V/m$ $E_x = 3.7~V/m$